Theorem equtr 1118

Description: A transitive law for equality.

Assertion

Ref	Expression
equtr	|- (x = y -> (y = z -> x = z))

Proof of Theorem equtr

Step	Hyp	Ref	Expression
1		ax-8 1101	. 2 |- (y = x -> (y = z -> x = z))
2	1	equcoms 1117	1 |- (x = y -> (y = z -> x = z))

Syntax hints:   -> wi 3   = wceq 1099

This theorem is referenced by:  equtrr 1119  equtr2 1120  equequ1 1121  equvin 1257  a12lem1 1353  axsep 2670  dscmet 7804

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-gen 955  ax-8 1101  ax-9 1102  ax-12 1104

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 957

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